ACR FLT TAKES DSCNT CLRNC FOR COMPANY ACFT AND CAUSES LTSS. CTLR DID NOT HEAR ERRANT READBACK.

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ISSUED CLRNC TO ACR 'ABCD' TO DSND TO FL260. COMPANY FLT 'EFD' TOOK CLRNC AND DSNDED INTO ACR 'XY' AIRSPACE AT FL280. I TURNED ACR 'EFD' TO 180 DEG HDG AND CLBED BACK TO FL290. ACR 'XY' MISSED HIS SLOT TIME WITH 'TMU.' IF ACR 'XY' HAD BEEN HELD ON THE GND OR IN APCH CTL'S AIRSPACE THE INCIDENT WOULD NOT HAVE HAPPENED. SUPPLEMENTAL INFO FROM ACN 249358: WE WERE TO GIVE ZTL 15 MI IN TRAIL SPACING AND POSSIBLY INCREASING. WE WERE GIVEN LESS THAN 10 MI IN TRAIL. MOST OF THE ACFT ON FREQ WERE BRAND 'X' AND A LOT OF THEM HAD SIMILAR SOUNDING CALL SIGNS. ONE OF THE BRAND 'X' WAS ASSIGNED AN ALT BUT A DIFFERENT BRAND 'X' WITH A SIMILAR CALL SIGN TOOK THE CLRNC AND DSNDED JUST BEHIND COMPANY AT THE NEXT FLT LEVEL BELOW HIM. CONTRIBUTING FACTORS POSSIBLY: NUMEROUS SIMILAR SOUNDING CALL SIGNS. INCREASED CTLR WORKLOAD DUE TO MI IN TRAIL RESTRS AND VERY LITTLE FLOW CTL ASSISTANCE (1 ACFT MISSED HIS TIME SLOT ON THE GND BUT WAS PERMITTED TO DEPART ANYHOW. WE WERE TO SOMEHOW 'FIT HIM IN'). PLTS NOT LISTENING CAREFULLY WHEN IT IS CLEAR THAT THEY ARE IN THE MIDST OF A COMPANY PUSH WITH OTHER COMPANY SIMILAR SOUNDING CALL SIGNS ALSO ON FREQ. SUPPLEMENTAL INFO FROM ACN 249657: WHEN WE WERE SWITCHED OVER TO ZDC THE VECTORS CONTINUED. AT TIMES WE WERE GIVEN HDG CHANGES AS MUCH AS 100 DEGS. THE VECTORING WAS FOR IN TRAIL SPACING INBOUND TO CLT. WE HAD ALSO NOTICED THAT THERE WERE A NUMBER OF FLTS WITH VERY SIMILAR CALL SIGNS. A LOT OF THEM ENDING IN THE 'D.' WE HAD A 3 DIGIT CALL SIGN. MATTER OF FACT; THERE WAS 1 FLT THAT HAD A 3 DIGIT CALL SIGN AND 2 OF ITS 3 DIGITS WAS THE SAME AS OURS. BOTH OF THE CALL SIGNS ENDED WITH THE 'D.' AS WE PROCEEDED INBOUND TO LYH AT FL290 WE WERE RESTR TO 250 KTS. WE FOLLOWED OUR COMPANY'S STANDARD PROC OF ASSIGNED ALT CHANGES AND STARTED OUR DSCNT. AS WE STARTED A SLOW DSCNT WE VISUALLY SPOTTED THE TFC WE WERE FOLLOWING 1200 FT AND ABOUT 3.5 MI. PASSING THROUGH ABOUT FL285; CTR TOLD US TO MAINTAIN FL290 AND THAT WE HAD TFC AT 12 O'CLOCK; 3.5 MI; AND AT FL280. WE INFORMED THE CTR THAT WE HAD READ BACK OUR CLRNC TO FL260 FOLLOWED BY OUR CALL SIGN. APPARENTLY WE HAD TAKEN THE CLRNC FOR ANOTHER FLT WHOSE CALL SIGN ENDED IN THE 'D.' MANY OF THE SIMILAR CALL SIGNS HAD THE SAME AIRLINE PREFIX. THIS BECOMES A REAL PROB GOING THROUGH YOUR AIRLINE HUB. YOU MAY CHANGE FROM ONE ACFT TO ANOTHER; BOTH WITH SIMILAR CALL SIGNS. THIS CAN BE A POTENTIAL PROB IF YOU ARE BOTH DEPARTING ABOUT THE SAME TIME. SECONDLY; JUDGING FROM ALL THE AIRSPD AND HDG CHANGES WE RECEIVED THAT MORNING; IT APPEARED THAT WASHINGTON HAD MORE ACFT THAN IT COULD HANDLE. WHEN WE READ THE CLRNC BACK TO THE CTLR WE DID NOT GET A CONFIRMATION THAT HE GOT THE READBACK.